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M2 - Parcours Probabilitťs et ModŤles Alťatoires

The M2 - Parcours Probabilitťs et ModŤles Alťatoires is a high-level theoretical training program in the field of probabilities. The program is divided into two semesters, with the first semester providing a foundation in the fundamental aspects of the field and the second semester offering specialized courses.

Organisation

• First Semester (30 ECTS), September-January: The semester begins with an intensive pre-entry course in September, which reviews the knowledge of probabilities acquired in M1.
  • For students who have chosen the "Processus stochastiques" orientation:
    • "Processus de Markov et Applications" (9 ECTS)
    • "Calcul Stochastique et Processus de Diffusions" (9 ECTS)
    • "ThťorŤmes Limites pour des Processus Stochastiques" (6 ECTS)
    • One elective course: "Nuages Poissioniens, Processus de Levy et Excursions" (6 ECTS) or "Statistique et Apprentissage" (6 ECTS)
  • For students who have chosen the "Probabilitťs Appliquťes" orientation:
    • "ModŤles Markoviens sur des espaces discrets" (6 ECTS)
    • "Calcul Stochastique et Processus de Diffusions" (9 ECTS)
    • "Probabilitťs numťriques et Mťthodes de Monte Carlo" (9 ECTS)
    • "Statistique et Apprentissage" (6 ECTS)
• Second Semester (30 ECTS), February-June: Students have the choice among specialized courses:
  • "Probabilitťs, AlgŤbre et Thťorie Ergodique" (6 ECTS)
  • "Probabilitťs et Physique" (6 ECTS)
  • "Probabilitťs, Mťthodes Numťriques, Algorithmes et Internet" (6 ECTS)
  • "Mťthodes Stochastiques et Statistiques II" (6 ECTS)
  • "Gťomťtrie Alťatoire" (6 ECTS)
  • "Probabilitťs, Neurosciences et Sciences Mťdicales" (6 ECTS)
  • "Probabilitťs, Biologie et Analyse des Graphes" (6 ECTS)

Public Visť

This specialty is aimed at students coming from the M1 in mathematics and holders of a master's degree in Mathematics, Applied Mathematics, or Mathematical Engineering. It is also open to holders of a master's degree M.A.S.S. or an engineering diploma (or possibly two years of study in an engineering school), subject to sufficient training in mathematics, particularly in probabilities.

Admission

The main selection criterion is a solid prerequisite in general mathematics, and in particular in measure theory and integration, and probability calculus.

Dťbouchťs

The primary vocation of the specialty is to train future researchers in probability calculus. For this reason, the majority of students who succeed in this specialty then orient themselves towards a Doctorate, the third component of the LMD, by preparing a thesis.

Several students prepare a thesis within the Laboratoire de Probabilitťs Statistiques et Modťlisation. This laboratory of Sorbonne Universitť and Universitť de Paris, associated with the CNRS, ensures the implementation of the specialty. It is one of the most active research centers in the world in the field of probabilities and stochastic processes.

Students can also prepare a thesis within other research laboratories (university or grande ťcole) as well as in research institutes (INRIA, INRA, and others) in France and abroad. People who have chosen the Probabilitťs Appliquťes orientation do so in a company under the form of CIFRE contracts (ORANGE, EDF, CEA, AREVA, SAFRAN, SCHLUMBERGER, ...).

This training also provides immediate professional outlets in companies, particularly in banks, insurance companies, or financial institutions.

This master's degree is also a career asset for mathematics teachers in high schools and preparatory classes.